I say, Yes.
It's not always easy to tell whether a creature is using its Strength or Dexterity for its attacks. It's really up to the DM to decide how a creature fights and if a Strength drain affects its fighting ability.
Compare the creature's Challenge Rating on page 8 of the Monster Manual to find what its Proficiency Bonus is. From that we can compare it's Dexterity and Strength Modifiers to make a guess. Thankfully in the case of the Giant Scorpion, it looks pretty clean cut to me.
The Giant Scorpion has a Challenge Rating of 3. As per the Monster Manual (pg. 8), that gives it a Proficiency Bonus of +2.
It's Dexterity and Strength Modifiers are +1 and +2 respectively. To get its Attack Bonus of +4, it would probably have to use its Strength. Its damage dice are also modified by +2 which seems to lean towards a Strength based attack.
That's just my thoughts on this. Ultimately, it's up to the DM of your group to decide exactly which creatures use which stats to fight with as it's often not clear from the creature description.